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arXiv · 1406.7105

Poisson structures on smooth 4-manifolds

Luis C. García-Naranjo·Pablo Suárez-Serrato·Ramón Vera
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Abstract

We show that every closed oriented smooth 4-manifold admits a complete singular Poisson structure in each homotopy class of maps to the 2-sphere. The rank of this structure is 2 outside a small singularity set, which consists of finitely many circles and isolated points. The Poisson bivector has rank 0 on the singularities, where we give its local form explicitly.

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Luis C. García-Naranjo, Pablo Suárez-Serrato, Ramón Vera. 2015-03-27. Poisson structures on smooth 4-manifolds. https://doi.org/10.1007/s11005-015-0792-8

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